Write the ratio 20 inches to 3 feet using fractional notation. Simplify the fraction to lowest terms. Use 1 foot = 12 inches to first write feet as inches.
A. 5/9
B. 20/3
C. 3/20
D. 9/5
How do you write 1 is to 2 as 5 is to x as a proportion in fractional notation?
A. 2/1 = 5/x
B. 1/2 = 5/x
C. 1 : 2 = 5 : x
D. 1 : 3 :: 5 : x
Determine if 2.25/10 ?= 9/40' 2.5/10 ?= 90/40' or 2.25/12 ?= 90/40 is a proportion.
A. None of these sets of ratios is a proportion.
B. 2.25/10 = 9/40
C. 2.25/12 = 90/40
D. 2.5/10 = 90/40
Meters Feet
7 23.03
6 19.74
5 16.45
4 13.16
Determine the number of feet in 1 meter.
A. 3.29 feet
B. 4/13.16 foot
C. 161.21 feet
D. 0.304 feet
You made 280.00 for working 40, which is described by 40y = $280.00x. Determine your earnings per hour.
A. $0.14
B. $70.00
C. $11,200
D. $7.00
(10, 5)
(8, 4)
(4, 2)
The proportional relationship is shown on the graph. Derive the equation of the line y = mx through the origin.
A. y = 4x
B. y = 1/2x
C. y = 2x
D. y = 8x
Graph the proportional relationship y = x by plotting points.
A.
(0, 0)
(1, -1)
(2, -2)
B.
(2, 2)
(0, 0)
(1, 1)
C.
(2, 4)
(1, 2)
(0, 0)
D.
(3, 1)
(0, 0)
(0, 0)
(100, 5)
(200, 10)
(300, 15)
The graph displays the number of miles a car traveled and the gallons of gasoline used. Determine the average miles per gallon.
A. The car averaged 4,500 miles per gallon.
B. The car averaged 15 miles per gallon.
C. The car averaged 300 miles per gallon.
D. The car averaged 20 miles per gallon.
Employee 1 - Earnings per Hour Employee 2 - Earnings per Hour
(0, 0) (0, 0)
(30, 2) (30, 3)
(45, 3) (40, 4)
(60, 4) (50, 5)
Two employees tracked their earnings and hours that they worked. The graphs document the earnings for Employee 1 and Employee 2. Which employee earns more per hour?
A. Employee 1, because Employee 1 earns $30 per hour and Employee 2 earns $10 per hour.
B. Employee 1, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour.
C. Employee 2, because Employee 1 earns $15 per hour and Employee 2 earns $30 per hour.
D. Employee 2, because Employee 1 earns $10 per hour and Employee 2 earns $15 per hour.
(0, 0)
(1, -3)
(2, -6)
(3, -9)
What is the slope of the line?
A. -6
B. -1
C. -3
D. 3
A. 5/9
Write the ratio 12 : 9 as an equivalent ratio 4 : x.
To find the value of x, we can set up a proportion:
12/9 = 4/x
To solve for x, we can cross-multiply:
12x = 9 * 4
12x = 36
Now, we can divide both sides by 12 to solve for x:
x = 36/12
Simplifying, x = 3
Therefore, the equivalent ratio is 4 : 3.
There are 48 inches in 4 feet, which is represented by the equation 4y = 48x. Determine the number of inches per foot.
To find the number of inches per foot, we need to determine the value of y in the equation 4y = 48x.
First, we divide both sides of the equation by 4:
4y/4 = 48x/4
y = 12x
Now we can see that the ratio of inches to feet is 12 inches to 1 foot, or 12 : 1.
(10, 2)
(5, 1)
Derive the equation of the line y = mx through the origin.
To derive the equation of the line y = mx through the origin, we need to find the value of m, which represents the slope of the line.
The slope of a line can be calculated using the formula:
m = (change in y) / (change in x)
Let's calculate the change in y and change in x using the given points (10, 2) and (5, 1):
Change in y = 1 - 2 = -1
Change in x = 5 - 10 = -5
Now, we can calculate the slope:
m = (-1) / (-5)
When dividing a negative number by a negative number, the negatives cancel out:
m = 1/5
Therefore, the equation of the line y = mx through the origin is y = (1/5)x.
Graph the proportional relationship y = 2x by plotting points.
A.
(1, 4)
(0, 0)
B.
(2, 4)
(1, 2)
(0, 0)
C.
(2, 6)
(1, 3)
(0, 0)
D.
(2, 1)
(0, 0)
To graph the proportional relationship y = 2x, we can choose any values for x and calculate the corresponding values for y.
Let's choose a few values for x and calculate y:
For x = 0, y = 2(0) = 0. This gives us the point (0, 0).
For x = 1, y = 2(1) = 2. This gives us the point (1, 2).
For x = 2, y = 2(2) = 4. This gives us the point (2, 4).
Plotting these points on the graph, we can see that they lie on a straight line.
Therefore, the correct option is B.
(2, 4)
(1, 2)
(0, 0)
(0, 0)
(36, 3)
(72, 6)
(108, 9)
(144, 12)
The proportional relationship between calories and ounces of soda is shown in the graph. How many calories are in 1 ounce?
There are __ calories in 1 ounce of soda.
To find the number of calories in 1 ounce of soda, we need to determine the value of y for x = 1 in the given graph.
From the given points, we can see that for every 36 ounces of soda, there are 3 calories.
So, for 1 ounce of soda, we can set up a proportion:
36 ounces / 3 calories = 1 ounce / y calories
To solve for y, we can cross-multiply:
36y = 3 * 1
36y = 3
Now, we can divide both sides by 36 to solve for y:
y = 3/36
Simplifying, y = 1/12
Therefore, there are 1/12 or 0.083 (rounded to three decimal places) calories in 1 ounce of soda.
Employee 1 - Earnings per Hour Employee 2 - Earnings per Hour
(0, 0) (0, 0)
(25, 2) (15, 1)
(50, 4) (45, 3)
(75, 6) (75, 5)
The earnings for Employee 1 and Employee 2 are displayed in the following graphs. Which employee earns more per hour?
Employee __ earns more per hour.
To determine which employee earns more per hour, we can compare the rates at which their earnings increase over time. The rate of earnings is calculated by dividing the change in earnings by the change in hours worked.
For Employee 1:
Rate of earnings = (Change in earnings) / (Change in hours worked)
Between (0, 0) and (50, 4):
Change in earnings = 4 - 0 = 4
Change in hours worked = 50 - 0 = 50
Rate of earnings for Employee 1 = 4 / 50 = 0.08
For Employee 2:
Rate of earnings = (Change in earnings) / (Change in hours worked)
Between (0, 0) and (45, 3):
Change in earnings = 3 - 0 = 3
Change in hours worked = 45 - 0 = 45
Rate of earnings for Employee 2 = 3 / 45 ≈ 0.067
Comparing the rates of earnings, we can see that Employee 1 has a higher rate of earnings at 0.08 per hour, compared to Employee 2 at 0.067 per hour.
Therefore, Employee 1 earns more per hour.
(3, 9)
(2, 6)
(1, 3)
(0, 0)
Use similar triangles to determine the slope of the line.
The slope is __
To determine the slope of the line using similar triangles, we can consider the ratios of the corresponding side lengths of the triangles formed by the given points.
Let's take two consecutive points, (3, 9) and (2, 6), on the line:
The change in y is 6 - 9 = -3.
The change in x is 2 - 3 = -1.
Next, let's take two consecutive points, (2, 6) and (1, 3):
The change in y is 3 - 6 = -3.
The change in x is 1 - 2 = -1.
We can see that the ratios of the changes in y to the changes in x are the same for both pairs of points, indicating that the line is a straight line and has a constant slope.
So, the slope of the line can be determined by taking any pair of consecutive points and finding the ratio of the change in y to the change in x.
For the points (3, 9) and (2, 6):
Slope = (change in y) / (change in x) = (-3) / (-1) = 3
Therefore, the slope of the line is 3.
How could you write the equation of a line that would be parallel to y = -3x - 2 but not share any points?
To write the equation of a line that is parallel to y = -3x - 2 but does not share any points, we need to keep the same slope but choose a different y-intercept.
The slope of the line y = -3x - 2 is -3. Since parallel lines have the same slope, the line we want to find will also have a slope of -3.
To determine the y-intercept, we can choose any point that lies on the line but is not shared with y = -3x - 2. Let's choose the point (0, 5) as an example.
Using the point-slope form of a linear equation, we can write the equation of the line that is parallel to y = -3x - 2 and passes through the point (0, 5) as:
y - 5 = -3(x - 0)
Simplifying:
y - 5 = -3x
y = -3x + 5
Therefore, the equation of the line that is parallel to y = -3x - 2 but does not share any points is y = -3x + 5.
not an answer
Apologies for the confusion. I misspoke in my previous response.
To write the equation of a line that is parallel to y = -3x - 2 but does not share any points, we can keep the same slope but choose a different y-intercept.
The slope of the line y = -3x - 2 is -3. Since parallel lines have the same slope, our parallel line will also have a slope of -3.
To ensure that the line does not share any points, we can choose any point not on the line y = -3x - 2. Let's choose the point (0,1) as an example.
Using the point-slope form of a linear equation, the equation of the parallel line can be written as:
y - y1 = m(x - x1)
Substituting the values of the point (0,1) and the slope -3, we get:
y - 1 = -3(x - 0)
Simplifying:
y - 1 = -3x
y = -3x + 1
Therefore, the equation of a line that is parallel to y = -3x - 2 but does not share any points is y = -3x + 1.
How could you write the equation of a line that would be parallel to y = -3x - 2 but not share any points?
A. y = -3x - 2
B. y = - 3x + 8
C. y = 3x - 2
D. y = 3x + 8
To write the equation of a line that is parallel to y = -3x - 2 but does not share any points, we need to keep the same slope but choose a different y-intercept.
The given equation y = -3x - 2 is in the slope-intercept form (y = mx + b), where m is the slope (-3) and b is the y-intercept (-2).
Since we want to keep the same slope, the equation of the line parallel to y = -3x - 2 will also have a slope of -3.
To determine the y-intercept of the new line, we can choose any value for the y-intercept as long as it is different from -2.
Option B, y = -3x + 8, has the same slope (-3), but a different y-intercept (8) compared to the given equation.
Therefore, the equation of a line that is parallel to y = -3x - 2 but does not share any points is y = -3x + 8.
($) Cost of Candy Bar 1
Quantity ($) Cost
1 1.25
2 2.50
3 3.75
4 5.00
5 6.25
The cost of Candy Bar 1 is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar 2 is represented by the equation y = x. Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar 1. Enter 2 for Candy Bar 2.
To determine which candy bar is the cheapest cost per bar, we need to compare the cost per bar for both Candy Bar 1 and Candy Bar 2.
In the table provided, we can see that the cost of Candy Bar 1 increases by $1.25 for each additional quantity. This indicates that the cost is not proportional to the quantity, as the ratio of cost to quantity is not constant.
On the other hand, for Candy Bar 2, the equation y = x represents a proportional relationship between the cost and quantity. This means that the cost increases at the same rate as the quantity.
Since the cost of Candy Bar 2 increases at a constant rate, it can be considered the cheapest cost per bar. Therefore, the answer is:
The cheapest cost per bar is for Candy Bar 2, so you should enter "2" for Candy Bar 2.
(1, 3)
(0, -2)
Derive the equation of the line in slope-intercept form.
To derive the equation of the line in slope-intercept form, we can use the given points (1, 3) and (0, -2) to find the slope and the y-intercept of the line.
We can start by calculating the slope (m) using the formula:
m = (change in y) / (change in x)
For the points (1, 3) and (0, -2):
Change in y = 3 - (-2) = 5
Change in x = 1 - 0 = 1
Therefore, the slope (m) is:
m = 5/1 = 5
Next, we can substitute one of the given points and the slope into the slope-intercept form of a linear equation, which is:
y = mx + b
Using the point (1, 3):
3 = 5(1) + b
Simplifying:
3 = 5 + b
Now, we can solve for the y-intercept (b):
b = 3 - 5 = -2
Therefore, the y-intercept (b) is -2.
Now that we have the slope (m = 5) and the y-intercept (b = -2), we can write the equation of the line in slope-intercept form:
y = 5x - 2
So, the equation of the line is y = 5x - 2.
Graph the linear equation y = 2x - 3.
To graph the linear equation y = 2x - 3, we can start by creating a table of values for x and corresponding values for y. Let's choose some values for x:
|x |y |
|---|---|
| -2 | -7 |
| -1 | -5 |
| 0 | -3 |
| 1 | -1 |
| 2 | 1 |
Next, we can plot these points on the coordinate plane
Graph the linear equation y = 2x - 3.
A.
(0, -1)
(1, -3)
B.
(1, 5)
(0, 3)
C.
(1,4)
(0,1)
D.
(1,-1)
(0,-3)